Question

If the sum of a two digit number is 6. When we interchange the digits the original number comes to be 30 more than the new number. Find the two digit number.

Answer 1

Answer:

My present age will be 13 years

Solution:

From the given information,

Let my present age be taken as x

My sister’s age be taken as y

My father’s age will be taken as z

Given,

$\begin{array} { c } { x = 2 + y } \\\\ { z = 2 x } \\\\ { ( z - 5 ) - 13 = ( x - 5 ) } \end{array}$

Thus,

$\begin{array} { c } { z - 5 - 13 = x - 5 } \\\\ { z - 18 = x - 5 } \\\\ { z - x = 18 - 5 } \\\\ { z - x = 13 } \end{array}$

Substituting z=2x in the above equation, we get

$\begin{array} { c } { 2 x - x = 13 } \\\\ { \quad x = 13 } \end{array}$

Substitute the value of x = 13 in equation $x=2+y$, we get

$\begin{array} { c } { x = 2 + y } \\\\ { 13 = 2 + y } \\\\ { y = 13 - 2 = 11 } \end{array}$

Thus,

$z = 2 x = 2 \times 13 = 26$

Hence,  

Age of my father = 26 years

Age of my sister = 11 years

Thus, my present age will be 13 years